Answer:
14b and 14d require renaming mixed numbers; 14a) 3 3/20; 14b) 2 1/8; 14c) 1 13/24; 14d) 3 3/6 = 3 1/2
Step-by-step explanation:
14a) First we find the least common denominator (LCD). The first thing that both 5 and 4 will divide into is 20; this is our LCD.
It takes 4 5's to make 20; multiplying the numerator by 4, we have 5 8/20. It takes 5 4's to make 20; multiplying the numerator by 5, we have 2 5/20. Subtracting these,
5 8/20 - 2 5/20 = 3 3/20
14b) We must write the whole number 5 as a mixed number with a denominator of 8; 5 = 4 8/8. This gives us
4 8/8 - 2 7/8 = 2 1/8
14c) The LCD of 3 and 8 is 24. It takes 8 3's to make 24; multiplying the numerator by 8, we have 7 16/24. It takes 3 8's to make 24; multiplying the numerator by 3, we have 6 3/24. Subtracting we have
7 16/24 - 6 3/24 = 1 13/24.
14d) The LCD of 6 and 3 is 6. Since the first mixed number has a denominator of 6, we leave it: 9 1/6. It takes 2 3's to make 6; multiplying the numerator by 2, we have 5 4/6. Subtracting we would have
9 1/6 - 5 4/6
We are subtracting a larger fraction from a smaller one. This means we borrow a whole from the whole number, making it 8; this makes the fraction (6+1)/6 = 7/6. This gives us
8 7/6 - 5 4/6 = 3 3/6 = 3 1/2
